Question

Va rog ajutatima cu ex: 31




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Answer 1

Răspuns:

Explicație pas cu pas:

a = 1 + 3 + 5 + ... + 99

b = 2 + 4 + 6 + ... + 100

_______________________

a) a + b = ?

b) a = pp (pătrat perfect)

a)

a = 1 + 3 + 5 + ... + 99

= (1 + 2 + 3 + ... + 99) - (2 + 4 + 6 + ... + 98)

= [99 × (99 + 1) ÷ 2] - 2 × (1 + 2 + 3 + ... + 49)

= (99 × 100 ÷ 2) - 2 × [49 × (49 + 1) ÷ 2]

= (9900 ÷ 2) - 2 × (49 × 50 ÷ 2)

= 4950 - 2 × (2450 ÷ 2)

= 4950 - 2 × 1225

= 4950 - 2450

= 2500

b = 2 + 4 + 6 + ... + 100

= 2 × (1 + 2 + 3 + ... + 50)

= 2 × [50 × (50 + 1) ÷ 2]

= 2 × (50 × 51 ÷ 2)

= 2 × (2550 ÷ 2)

= 2 × 1275

= 2550

(am aplicat suma lui Gauss-->N × (N + 1) ÷ 2)

a + b = 2500 + 2550

= 5050

b) a = 2500

$\sqrt{2500} = \sqrt{25} \times \sqrt{100 } = 5 \times 10 = 50$

a = ${50}^{2}$=> a = pp (pătrat perfect)